What Is an Oblique Asymptote?

An oblique asymptote is a linear asymptote that is not parallel to either the x- or y-axis. It is also called a slant asymptote. Oblique asymptotes always occur for rational functions when the numerator has a degree that is exactly one greater than the numerator.

A rational function is any function that is written as a ratio of two polynomials. For example, take the rational function y = (3x^2 + 2)/(x + 1). Because x is raised to the second power in the numerator, and only to the first power in the denominator, its degree difference is exactly one greater, resulting in asymptotes that are neither vertical nor horizontal. To find the linear equation for a slant asymptote, divide the numerator by the denominator and discard the remainder.